Electromagnetic Duality Sensitivity of Holographic Complexity

Abstract

We investigate electromagnetic duality as a diagnostic of the sensitivity of information content of holographic complexity via "complexity=anything" in Einstein-ModMax theory. Functionals constructed solely from gravitational invariants are duality invariant, whereas matter-sensitive functionals can distinguish electromagnetic configurations that share the same bulk geometry and energy-momentum tensor. As an explicit example, we consider a functional involving $F_{μν}F^{μν}$ and show that its complexity and complexity growth vary along the duality orbit, interpolating between purely electric, mixed electric-magnetic, and purely magnetic configurations. This provides an explicit realization of the freedom inherent in generalized holographic complexity and shows that different choices of complexity functional can retain different sensitivity to information about the bulk matter sector even when the gravitational geometry is insensitive to that information.